Abstract : In the analog VLSI implementation of neural systems, it is sometimes convenient to build lateral inhibition networks by using a locally connected on-chip resistive grid. A serious problem of unwanted spontaneous oscillation often arises with these circuits and renders them unusable in practice. This paper reports a design approach that guarantees such a system will be stable, even though the values of designed elements and parasitics elements in the resistive grid may be unknown. The method is based on a rigorous, somewhat novel mathematical analysis using Tellegens theorem and the idea of Popov multipliers from control theory. It is thoroughly practical because the criteria are local in the sense that no overall analysis of the interconnected system is required, empirical in the sense that they involve only measurable frequency response data on the individual cells, and robust in the sense that unmodelled parasitic resistances and capacitances in the interconnection network cannot affect the analysis.